{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import expon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "expected_travel_distance = 5.0   #小石を踏むまで進む量の期待値\n",
    "p = expon(scale=expected_travel_distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "zs = np.arange(0, 10, 0.01)\n",
    "ys = [p.pdf(z) for z in zs]\n",
    "\n",
    "plt.plot(zs,ys)\n",
    "plt.title(\"probaility density function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ys = [p.cdf(z) for z in zs]\n",
    "\n",
    "plt.plot(zs,ys)\n",
    "plt.title(\"cumulative distribution function\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
